Question

Isla, Bob and Marie are playing a game involving counters. The total number of counters stays the same throughout the game. At the start of the game, the ratio of Isla's counters to Bob's counters to Marie's counters is 5: 4:3. At the end of the game, this ratio is 6:57. Isla ends the game with 12 counters. How many counters did Isla start the game with?​

Answer 1

• 15 counters

Explanation:

Using the ratio and Isla's counters' number, find the total number of counters.

Let the multiplier be x, then the ratio is 6x : 5x : 7x, where Isla's number is 6x, which is 12.

• 6x = 12
• x = 2

Total number of counters is:

• (6 + 5 + 7)*2 = 36

Find the multiplier using initial ratios:

• 36 ÷ (5 + 4 + 3) =
• 36 ÷ 12 =
• 3

Find the initial number of counters Isla had:

• 5*3 = 15